Predicate modal logics with ω-rules are complete for neighborhood frames with constant domains under identified sufficient conditions, extending prior results on normal and non-normal modal logics.
Some proof systems for predicate common knowledge logic.Reports on Mathematical Logic, 37:79–100, 2003
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Neighborhood and algebraic models for predicate modal logics with $\omega$-rules
Predicate modal logics with ω-rules are complete for neighborhood frames with constant domains under identified sufficient conditions, extending prior results on normal and non-normal modal logics.